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Midpoint Property
If (x1, y1) and (x2, y2) are the coordinates of the endpoints of a segment, then the coordinates of the midpoint are: (X plus X divided by 2, and, Y plus Y divided by 2) Labeled as a coordinate pair (X, Y).
Undefined terms of Geometry
point, line, plane
Collinear Points
points that lie on the same line
Coplanar Points
points that lie on the same plane
Line Segment
consists of two points called the endpoints and all the points in between them that are collinear with the two points
Congruent segments
segments that have the same measure or length
Midpoint of a segment
the point on the segment that is same distance from both endpoints, midpoint bisects the segment
Ray
Portion of a line that contains all the points on the line that are on the same side of the first letter as the second letter
Angle
Two noncollinear rays having a common endpoint.
Adjacent Angles
two angles that share a common vertex and side, but have no common interior points
Measure of an angle
the smallest amount of rotation about the vertex from one ray to the other.
Protractor
a geometry tool used to measure angles
Congruent Angles
two angles that have the same measure
Angle Bisector
a ray that contains the vertex and divides the angle into two congruent angles
Counterexample
an example that proves that a statement is false
Parallel Lines
lines in the same plane that never intersect
Perpendicular Lines
lines that intersect at right angles (90 degrees)
Skew Lines
lines that are not in the same plane and do not intersect
Acute Angle
an angle that measures greater than 0 degrees and less than 90 degrees
Right Angle
an angle that measures 90 degrees
Obtuse Angle
An angle that measures more than 90 degrees but less than 180 degrees
Straight Angle
an angle that measures 180 degrees
Linear Pair
two adjacent angles whose noncommon sides are opposite rays
Vertical Angles
angles formed by 2 intersecting lines; they share a common vertex not a side
Complementary Angles
two angles whose measures have a sum of 90 degrees
supplementary angles
two angles whose measures have a sum of 180 degrees
Polygon
a closed figure in a plane, formed by connecting line segments endpoint to endpoint with each segment intersecting exactly two others
Three Sided Polygon
Triangle
Four Sided Polygon
quadrilateral
Five Sided Polygon
pentagon
Six Sided Polygon
hexagon
Seven Sided Polygon
heptagon
Eight Sided Polygon
octagon
Nine Sided Polygon
nonagon
Ten Sided Polygon
decagon
Eleven Sided Polygon
undecagon
Twelve Sided Polygon
dodecagon
diagonal of a polygon
a line segment connecting two nonconsecutive vertices of a polygon
convex polygon
a polygon with no diagonal outside the polygon
Concave Polygon
A polygon that has at least one diagonal with points outside the polygon.
congruent polygons
two polygons whose corresponding sides and angles are congruent
equilateral polygon
a polygon in which all sides are congruent
equiangular polygon
A polygon with all angles have same measure
Regular Polygon
a polygon that is both equilateral and equiangular
Right Triangle
a triangle that has one right angle
acute triangle
A triangle with 3 acute angles
obtuse triangle
a triangle with one obtuse angle
scalene triangle
a triangle with no congruent sides
equilateral triangle
A triangle with three congruent sides
Isosceles Triangle
a triangle with at least two congruent sides
Trapezoid
A quadrilateral with exactly one pair of parallel sides
Kite
a quadrilateral with two distinct pairs of consecutive congruent sides
Parallelogram
A quadrilateral with two pairs of parallel sides
Rhombus
an equilateral parallelogram (all congruent sides, 2 pairs of parallel sides)
Rectangle
an equiangular parallelogram (all congruent angles, 2 pairs of parallel sides)
Square
an equilateral rectangle or an equiangular rhombus or a regular quadrilateral
Circle
The set of all points in a plane that are the same distance from a given point called the center
Radius
The distance from the center of a circle to any point on the edge of a circle
Diameter
A line segment that passes through the center of a circle and has endpoints on the circle
Secant
A line that intersects a circle in two points
chord
A segment whose endpoints lie on a circle
Tangent
A line in the plane of a circle that intersects the circle in exactly one point.
point of tangency
the point where a circle and a tangent intersect
congruent circles
Two or more circles that have the same radius
concentric circles
2 or more coplanar circles with the same center
arc of a circle
two points on the circle and the continuous part of the circle between the two points
semicircle
an arc with endpoints that are the endpoints of a diameter
minor arc
an arc that is less than a semicircle
Major Arc
an arc that is greater than a semicircle
Central Angle
an angle with its vertex at the center of a circle
arc measure
the measure of the corresponding central angle
Note
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